Polynomials: Terms and Degree
Sums of terms cxⁿ; the degree is the highest power.
Key idea
Sums of terms cxⁿ; the degree is the highest power.
In depth
A polynomial is a sum of terms with non-negative integer powers. The degree is the highest power; the leading coefficient multiplies that term. Degree determines the shape and the number of roots.
Worked example
3x⁴ − 2x + 7 has degree 4, leading coefficient 3, constant term 7.
Real-world uses
- Modelling the path of a ball or a cost curve
- Describing shapes of graphs
Common mistake
Including terms with negative or fractional powers as polynomials.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Polynomials: Terms and Degree?
Sums of terms cxⁿ; the degree is the highest power. It is a topic at the intermediate level in Algebra.
Where is Polynomials: Terms and Degree used in real life?
Real-world examples: Modelling the path of a ball or a cost curve; Describing shapes of graphs.
What should I learn before Polynomials: Terms and Degree?
Make sure you are comfortable with Exponent Rules for Variables, the previous topic in Algebra.
What is a common mistake with Polynomials: Terms and Degree?
Including terms with negative or fractional powers as polynomials.
How can I practise Polynomials: Terms and Degree?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Polynomials: Terms and Degree?
Move on to Adding and Subtracting Polynomials next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.